My evidence is as follows: This Page which lists animals allowed or not by state and links the laws that apply. First Link lists animals that are allowed with permit, does not list Emu either as requiring a permit or not allowed at all. Second Link which defines what a wild animal is.
Also, I live in Virginia which has much stricter laws about weird animals than TX and we are allowed Emu but if we want Ostrich we have to have a dangerous animals permit. So, I would imagine that TX probably doesn't consider Emu to be dangerous either.